Going by what the boat came with the boat is an odd approach. Start with what the Gypsy can take. You have no idea if anyone made any changes along the way.
Remove the gypsy and look on the side. The size is usually stamped there. I suspect you have a Lewmar V series (V1; V2; V3).
If this is the case, then the gypsy will be stamped with (001; 002; or 003)
Yours is probably an "002" which means it would take 5/16" G40.
V - Series V1/V2/V3
000
CHAIN 7mm ISO 4565, 7mm Din 766, 1/4" G40*, 1/4" BBB
ROPE SIZE (MM): 12-14
ROPE SIZE (IN): 1/2 3-strand and 8-plait
001
CHAIN 8mm DIN 766, 8mm ISO 4565
ROPE SIZE (MM): 12-16
ROPE SIZE (IN): 1/2 - 5/8 3-strand and 8-plait (5/8 only)
002
CHAIN 10mm DIN 766, Campbell 3/8" S4, 5/16" G40
ROPE SIZE (MM): 12-16
ROPE SIZE (IN): 1/2 - 5/8 3-strand and 8-plait (5/8 only)
003
CHAIN 10mm ISO, Campbell 3/8" S3, Lewmar 9.5mm G40
ROPE SIZE (MM): 16
ROPE SIZE (IN): 5/8 3-strand and 8-plait
006
CHAIN 6mm ISO 4565, 1/4" G40*, 1/4" BBB
ROPE SIZE (MM): 12-14
ROPE SIZE (IN): 1/2 3-strand and 8-plait
https://www.lewmar.com/Windlass-Gypsy-Guides